Question: Simplify the following expression: $p = \dfrac{-24x + 42}{-24x + 30}$ You can assume $x \neq 0$.
Answer: Find the greatest common factor of the numerator and denominator. The numerator can be factored: $-24x + 42 = - (2\cdot2\cdot2\cdot3 \cdot x) + (2\cdot3\cdot7)$ The denominator can be factored: $-24x + 30 = - (2\cdot2\cdot2\cdot3 \cdot x) + (2\cdot3\cdot5)$ The greatest common factor of all the terms is $6$ Factoring out $6$ gives us: $p = \dfrac{(6)(-4x + 7)}{(6)(-4x + 5)}$ Dividing both the numerator and denominator by $6$ gives: $p = \dfrac{-4x + 7}{-4x + 5}$